User:Yerevantsi/sandbox/Mergelyan


 * Sergey Mergelyan

ru:Мергелян, Сергей Никитович

Sergey Nikitovich Mergelyan (Сергей Никитович Мергелян; Սերգեյ Նիկիտի Մերգելյան; May 19, 1928 – August 20, 2008) was a Soviet Armenian mathematician.

Mergelyan's theorem

A child prodigy, Mergelyan graduated from Yerevan State University (YSU) at 19 and received a doctorate from the Steklov Institute of Mathematics at 20, becoming the Soviet Union's youngest Doctor of Science. He taught at YSU and Moscow State University. In 1956 he became the first director of the Yerevan Scientific Research Institute of Mathematical Machines, which became so closely associated with him that it was popularly known as the "Mergelyan Institute." He then mostly divided his time between Yerevan and Moscow until 1986, when he left Armenia, first settling in Moscow, then emigrating to the United States, where he died.

Early life
He was born Sergey Nikitovich Mergelov on May 19, 1928 in Simferopol, Crimea. His father, Mkrtich Mergelyan (1891–1955), was known by his russified name Nikita Ivanovich Mergelov. He was an Armenian originally from Akhalkalaki, Javakheti (Javakhk). He was a private employer specializing in the development of small industrial complexes. His mother, Lyudmyla Ivanovna Vyrodova (1902–1956), was the daughter of a bank manager executed by the Bolsheviks in 1918 in Berdyansk. Sergey spent his childhood years in Russia and Ukraine and did not speak Armenian. He studied at a secondary school in Kerch, Crimea.

In 1936 Sergey and his parents were sent to Narym, Tomsk Oblast in Siberia by the Soviet authorities, who declared his father a "NEPman" for building and operating a paper mill in Yelets, Lipetsk Oblast. Sergey and his mother were acquitted by a court decision in 1937 and returned to Kerch and successfully petitioned Soviet Prosecutor General Andrey Vyshinsky to release Nikita in 1938.

In 1941 his family moved to Yerevan, Soviet Armenia during the evacuation of Kerch during World War II, before the advance of the German forces. His father was invited to build a cardboard factory in Yerevan. Sergey, his parents and maternal grandmother lived in a 20 m2 apartment. He learned Armenian and began reciting Charents poems.

Education
Mergelyan was a child prodigy. He finished secondary school in Yerevan. At 16, Mergelyan passed the exams to graduate early and immediately enrolled at the Faculty of Physics and Mathematics of Yerevan State University in the fall of 1944. His first mentor was Artashes Shahinian, the founder of the Armenian school of mathematics. He finished his university studies in three and a half years instead of five, graduating in 1947. He changed his last name from the russified Mergelov to the original Armenian and received his university degree as Mergelyan.

In 1947 he moved to Moscow to continue his studies at the Steklov Institute of Mathematics of the USSR Academy of Sciences under Mstislav Keldysh. Keldysh often invited him to his home to discuss mathematics. Mergelyan wrote his thesis for the degree of candidate (kandidat) of physical and mathematical sciences in a year and a half. He defended it in 1949 and was awarded the degree of a doctor of physical and mathematical sciences, the highest scientific degree. All three official opponents: Sergey Nikolsky, Mikhail Lavrentyev and Alexander Gelfand requested the Academic Board, headed by Ivan Vinogradov, to award Mergelyan the doctoral degree instead of the degree of candidate for his outstanding contribution to the approximation theory. On February 17, 1949 the Academic Board voted unanimously to award Mergelyan, aged 20, a doctoral degree. Thus, Mergelyan became the youngest Doctor of Science in the Soviet Union.

Sergey Mergelyan was the youngest PhD in the history of the USSR (degree was awarded at the age of 20), the youngest corresponding member of the USSR Academy of Sciences (since 1953, the title was awarded at the age of 24), academician of Armenian Academy of Sciences (since 1956).

Research
Complex analysis, approximation theory, potential theory

Mergelyan's theorem

S. N. Mergelyan, Uniform approximations to functions of a complex variable (Russian). Uspekhi Mat. Nauk7, no. 2(48) (1952), 31-122; English transl in Amer. Math. Soc. Transl. (1) 3 (1962), 294-391.

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=8302&option_lang=eng

Область научных интересов: теория функций комплексного переменного.

Основные труды: «Некоторые вопросы конструктивной теории функций» (1951), «Советская математическая школа» (соавт., 1967).

His area of scientific interests was dealt with the approximate representations of given functions through simpler ones. This problem was first formulated by P. L. Chebyshev and applied to the theory of mechanisms, further it was developed by A. A. Markov (senior) and later by S. N. Bernstein, M. A Lavrentiev and M. V. Keldysh. Nevertheless, in the field of complex numbers the theory of approximations remained still little studied. Mergelyan engaged in research and received a number of brilliant results. In 1951-53 he published several important works: “Some questions of constructive theory of functions,” “Uniform approximations of complex variable functions,” “On the completeness of analytic functions systems” and proposed a solution for the approximation of continuous functions by polynomials. The level and importance of his works could also be assessed by the fact that in 1952 Sergey Mergelyan was awarded the Stalin (State) Prize of Second Degree with the payment of 100,000 rubles. The sum for those times was astronomical (it was possible to buy 6 passenger cars “Pobeda”). Commenting the awarding President of the USSR Academy of Sciences academician A. N. Nesmeyanov noted that Mergelyan’s work had: “Particular importance from the view point of using the results in the operation of large automatic computers.”

Mergelyan’s theorem which gives the complete solution of the problem of approximation by polynomials is recognized as classical [1]. All students who take the course “Theory of Functions” will study it.

In 1956 Mergelyan wrote articles “Weight approximations by polynomials” and “Harmonic approximation and approximate solution of Cauchy problem for Laplace equation.”

Область научных интересов С. Н. Мергеляна — теория приближения и представления функций комплексного переменного, теория наилучших приближений функций комплексного переменного, теория равномерного приближения функций комплексного переменного многочленами и рациональными функциями, проблемы среднеквадратичного приближения и полноты систем аналитических функций комплексного переменного сходящимися последовательностями аналитических функций, проблема наилучшей мажоранты, теория гармонических функций.

Основные труды С. Н. Мергеляна относятся к теории функций комплексного переменного, в частности к теории равномерного приближения многочленами и рациональными функциями комплексного переменного (теоремы Мергеляна). Создал свои методы приближения многочленами и рациональными функциями. В 1951 г. предложил решение задачи о приближении непрерывных функций полиномами. В 1954 г. решил аппроксимационную проблему Бернштейна. В 1962 г. изучил задачу о приближении функций, удовлетворяющих свойствам гладкости, для произвольного множества.

С. Н. Мергелян опубликовал монографии

О скорости приближения аналитических функций полиномами в замкнутых областях (1947); Некоторые вопросы конструктивной теории функций (1951); Равномерные приближения функций комплексного переменного (1952); О полноте систем аналитических функций (1953); Весовые приближения многочленами (1956); Избранные вопросы теории приближений (1966).

Мергелян был также талантливым организатором науки. В 1956-60гг. С. Мергелян был директором Научно- исследовательского института математических машин, который сегодня известен нам как "Институт Мергеляна".

В 1951, Сергей Мергелян доказал свою знаменитую теорему о приближении многочленами. Эта теорема завершила длинную серию исследований, начатую в 1885г. и составленную из классических результатов К. Вейерштрасса, К. Рунге, Дж. Уолша, M. Лаврентьева, M. Келдыша и других. Новые термины "Теорема Мергеляна" и "Множества Мергеляна" нашли свое место в учебниках и монографиях по теории приближений.

За эти выдающиеся исследования Мергеляну в 1952г. была присуждена Государственная премия СССР, а в следующем году 25-летний ученый был избран членом-корреспондентом АН СССР. В том же году он был избран членом- корреспондентом АН Арм. ССР, а в 1956 -- членом АН Арм. ССР.

Мергелян провел глубокие исследования и получил ценные результаты в таких областях как наилучшее приближение многочленами на произвольном континууме, весовые  приближения многочленами на вещественной оси, точечная аппроксимация многочленами на замкнутых множествах  комплексной плоскости, равномерное приближение  гармоническими функциями на компактных множествах и целыми функциями на неограниченном континууме,  единственность гармонических функций. В теории дифференциальных уравнений его результаты относились к сфере задачи Коши и некоторых других вопросов.

Научные достижения Мергеляна существенно способствовали становлению, развитию и международному признанию армянской математической школы, чему свидетельствовала  организованная в Ереване в 1965г. по инициативе и при активном участии С. Мергеляна крупная международная конференция по теории функций. В работе конференции приняли участие многие видные математики мира, что  способствовало международному сотрудничеству и дальнейшему продвижению армянской математической  школы.

His research was dealt with approximation of continuous functions satisfying the smoothness properties for an arbitrary set (1962) and the solution of Bernstein’s approximate problem (1963).

In MSU he published work “The Soviet Mathematical School” together with academician N. N. Bogolyubov.

Career
Mergelyan began working at the Institute of Mathematics of the Academy of Sciences of Armenian SSR in 1945 and worked there through 1957. He was initially a lab assistant, then junior and senior researcher. He taught at Yerevan State University (YSU) from 1949 to 1956 and at Moscow State University's Faculty of Mechanics and Mathematics from 1954 to 1958. Mergelyan was named professor at YSU in 1951.

Yerevan Institute of Mathematical Machines (1956–60)

 * User:Yerevantsi/sandbox/MergelyanInst

In 1956 Mergelyan was appointed director of the Yerevan Scientific Research Institute of Mathematical Machines (YerNIIMM). It was established on July 15, 1956 after the central authorities in Moscow approved the proposal of three prominent Armenian scientists—Viktor Ambartsumian, Artashes Shahinian, and Andronik Iosifyan, to establish a research institute specializing in design and production of electronic and computer machines. The institute became popularly known as the "Mergelyan Institute" and remains known by that name till today. Mergelyan headed the research institute until 1960. According to Apoyan, Ambartsumian had an indirect role in its establishment, while the central figure was Mergelyan.

In 1958–60 the Mergelyan Institute produced its first-generation computers called "Aragats", "Razdan-1" and "Yerevan". In 1958–61, "Razdan-2", the Soviet Union's first computer completely assembled on semiconductor devices was designed at the institute.

In 1957 Mergelyan founded and headed the joint Computing Center of Armenian Academy of Sciences and Yerevan State University (YSU).

In 1959 he published new work “Approximation of a complex variable functions” in jubilee collection of articles “Mathematics in the USSR for forty years: 1917-1957.” In April 1959 he visited the United States as a member of the Soviet delegation.

Mergelyan (1928-2008) was the youngest Ph.D. in the history of the USSR (his degree was awarded at the age of 20), the youngest corresponding member of the USSR Academy of Sciences (since 1953, the title was awarded at the age of 24), and the youngest academician of Armenian Academy of Sciences (since 1956). Mergelyan's theorem, which gives the complete solution of the problem of approximation by polynomials, is recognized as classical. He also played outstanding role in the history of Armenian computing.

Moscow (1960–71)
Mergelyan moved to Moscow in 1960 and continued to work at the Steklov Mathematical Institute of the USSR Academy of Sciences. In 1963 he was elected Deputy Secretary of Department of Mathematics of the Academy. In 1961 /1963 /1964 he became the the head of department of complex analysis at the Mathematical Institute, a position he held until 1971

In 1964–68 he also resumed teaching at the Faculty of Mechanics and Mathematics of Moscow State University.

В 1961–1986 гг. С. Н. Мергелян работал старшим научным сотрудником, заведующим Отделом комплексного переменного в МИАН. В 1964–1971 гг. — заместитель академика-секретаря Отделения математики АН СССР. Одновременно преподавал в МГУ — профессор механико-математического факультета 1964–1968 гг.

In 1962/63-65 and 1971-79 he headed the Computer Center of the Armenian Academy of Sciences and Yerevan State University.

С. Н. Мергелян — основатель (совместно с А. С. Кронродом) ведущей научной школы Российской Федерации «Комплексный анализ» Математического института им. В. А. Стеклова РАН. Руководители школы — Anatoli Georgievich Vitushkin (до 2004 г.) и E. M. Chirka.

Основатель (совместно с М. В. Келдышем и М. А. Лаврентьевым) ведущей научной школы Российской Федерации «Теория аппроксимаций в комплексном анализе» Математического института им. В. А. Стеклова РАН. Руководитель школы — Andrey Aleksandrovich Gonchar.

С 1967 г. в качестве члена редколлегии С. Н. Мергелян участвовал в издании журнала «Функциональный анализ и его приложения» АН СССР (РАН с 1991 г.).

Сергей Никитович Мергелян — представитель группы ученых, творческая деятельность которых развивалась в период, когда коллектив МИАН был ориентирован в значительной степени на развитие основных и новых направлений математики. Своими научными трудами содействовал формированию прочной позиции МИАН в отечественной науке.

Return to Armenia (1971–86)
In the 1970s Mergelyan continued to play a leading role in the organization of sciences in Soviet Armenia. In 1971–79 he headed the Computer Center of the Armenian Academy of Sciences and Yerevan State University. Between 1971 and 1974 he served as vice president of the Armenian Academy of Sciences, while the prominent astrophysicist Victor Ambartsumian was president. In 1972–79 he was chair of numerical analysis at Yerevan State University, and in 1979–82 he headed the department of complex analysis of the Institute of Mathematics of the Armenian Academy of Sciences.

In 1971 President of the Armenian Academy of Sciences Ambartsumyan managed to persuade Mergelyan to return to Armenia as Vice-President of the Academy. Mergelyan again moved to Yerevan. He was entrusted to completely uncharacteristic for him work on “extracting” money from Moscow and its distribution in the Armenian Academy. There was no better way to earn a lot of enemies in record time than this one. Almost all people were dissatisfied with the allocated money. Ingenuous Mergelyan did not recognize manipulations and to complete surprise of the majority of his colleagues Mergelyan in 1974 did not pass the next re-election to the Presidium of the Armenian Academy of Sciences and was forced to leave the Academy. There were many rumors that Ambartsumyan began to see in Mergelyan his competitor for the post of President of the Academy and invented this clever combination to get rid of the competitor forever. The shock from Mergelyan’s failure was so great that some academicians even suggested “revoting” the elections, but Ambartsumyan rebuffed.

After the failure in elections, Mergelyan returned to the Computing Center of Academy of Sciences which he had created and worked there for five years. Then he had to leave it as well. Mergelyan was blamed in “excessive interest in foreign (scientific) trips”. Perhaps he was really interested in frequent meetings with foreign colleagues, which affected the administrative affairs of the Center, but participation in congresses was the important source of the latest scientific information. Sergey Mergelyan lost this post and became the head of Department at the Institute of Mathematics of the Armenian Academy of Sciences. But he never interrupted communication with the USSR Academy of Sciences. For example, in 1981 together with N. N. Bogolyubov he published a special article on the 70th anniversary of his supervisor M. V. Keldysh under the title “On the mathematical works of M. V. Keldysh.”

In 1982 Mergelyan was appointed rector (president) of the Pedagogical Institute of Kirovakan, Armenia's third largest city. He served in that position until 1986. His appointment to this position was seen as a forced exile for "some sins." Oganjanyan and Silantiev describe it as as "humiliating."

Moscow and United States (1986–96)
In 1986 Mergelyan moved to Moscow, where he became a research associate at the Steklov Institute of Mathematics. In 1990 he moved to the United States, where he lectured at Brown University and later, in 1991-93 at Cornell University. Mergelyan returned to Moscow in 1993 and was named an adviser to the Russian Academy of Sciences in 1994. Unhappy with the situation in post-Soviet Russia, Mergelyan permanently left for the US in 1996. He lived with his son Nikita in Sacramento, California.

Personal life and death
From the mid-1950s to 1986, Mergelyan divided his time between Yerevan and Moscow. In the mid-1950s he was given a two-room apartment in Yerevan and an apartment in Moscow's Lenin Hills, within the new Moscow State University complex. He joined the Communist Party in 1955.

Mergelyan married Lydia Vasilievna Kulakova, a graduate of the Kharkov Institute of Theater and an actress at Moscow's Maly Theatre. They met in 1955 and married in 1956. Their wedding took place at the dacha of Andronik Iosifyan near Moscow. They had two sons: Nikita and Sergey. She died in 2002 and was buried at Moscow's Novodevichy Cemetery. Mergelyan spent his last years living with his youngest son's family in Los Angeles. He could hardly walk. He was visited there by his friends and colleagues.

Mergelyan died on August 20, 2008 at the Glendale Memorial Hospital in Glendale, California. The cause was heart failure. The Armenian National Academy of Sciences and President of Armenia Serzh Sargsyan sent their condolences. A farewell ceremony was held at Forest Lawn Memorial Park in Glendale on August 23. In accordance with his wishes, his cremated ashes were transported to Moscow and he was buried on October 12 in Moscow's Novodevichy Cemetery next to his mother and wife. His burial was attended by some 12 people. None of his children and no Armenian official attended it.

As a representative of Soviet science Sergey Mergelyan along with other his colleagues visited India, Italy and Australia. In India scientists were met by President Jawaharlal Nehru himself, who paid special attention to the young mathematician. There, in the picturesque park of the Osmania University, Mergelyan met with the American scientist Norbert Wiener, who said that he was familiar with the works of Mergelyan and admired them.

Mergelyan had a good singing voice and even seriously considered becoming an opera singer. "And in 1956 Mergelyan once again surprised everyone – he graduated from the conservatory in vocal class [2]."

Legacy and recognition


Mergelyan was among well-known Soviet mathematicians. In his 2016 book Andrew Targowski called Mergelyan "one of the most prominent mathematicians in the world." Radik Martirosyan, President of the Armenian Academy of Sciences, noted in 2018 that Mergelyan and Victor Ambartsumian are two Armenian scientists whose achievements are well-known worldwide. Georgi Derluguian and Ruben Hovhannisyan note that Mergelyan is one of the "modern icons of Armenian pride," along with Ambartsumian, Aram Khachaturian, Martiros Saryan, and Tigran Petrosian.

President of Armenia Serzh Sargsyan congratulated Mergelyan's 80th birthday in May 2008, noting that he has contributed immensely to the development of sciences in Armenia. Sargsyan awarded him the Order of St. Mesrop Mashtots on May 26, 2008. It was personally handed to Mergelyan by Armen Liloyan, Armenia's Consul General in Los Angeles on July 9.

Conferences dedicated to Mergelyan's 80th and 90th birthdays were held in Yerevan, Armenia in 2008 and 2018, respectively. In 2018 a commemorative plaque devoted to Mergelyan was placed on the Yerevan Computer Research and Development Institute. In a 2018 statement, Armenian president Armen Sarkissian noted that Mergelyan was "an individual and a scientist who not only knew the value of science but throughout his entire life and work was moving science forward, elevating and holding high the Armenian scientific thought. He made a unique contribution not only to the Armenian science but also to the Armenian economy."

his interests lie in theory of functions,

Prof. Norbert Weiner was close in the building, they asked if it would be possible to see him. Especially interested in seeing him was Mr. Mergelyan, who had met Prof. Wiener previously in India during one of the conferences attended by both. Prof. Buck volunteered to locate Prof. Wiener. Mr. Mergelyan's English, which is quite good, allowed the two to converse about their present work without the need of the interpreter.

T H E NEXT MORNING, May 1, Academician Lebedev, Mr. Bazilevskiy, and Mr. Petrov were taken to the IBM installation in Poughkeepsie, while Prof. Ditkin and Mr. Mergelyan were invited to give lectures at NYU.

Honors
1953թ. Ս.Մերգելյանն ընտրվել է ԽՍՀՄ ԳԱ և ՀԽՍՀ ԳԱ թղթակից անդամ, իսկ 1956թ.` ՀԽՍՀ ԳԱ ակադեմիկոս:

Laureate of the State award of the Union of Soviet Socialist Republics (1952). Was awarded with the Order of the Red Banner of Labour.

On October 23, 1953 Mergelyan was elected a corresponding member of the USSR Academy of Sciences, Department of Physical and Mathematical Sciences.

http://isaran.ru/?q=ru/person&guid=443F1C59-3B40-DB0B-84EB-4E6A3F8CB73B

Член-корреспондент АН СССР по Отделению физико-математических наук (математика) с 23 октября 1953 г.

Академик с 1956 г. и вице-президент АН Армянской ССР (ныне — Национальная АН Армении) в 1971–1974 гг.

В связи с разносторонней деятельностью и по случаю 80-летнего юбилея Сергей Мергелян в 2008г. был награжден орденом св. Месропа Маштоца.

Лауреат Государственной премии СССР (1952). Награжден орденом Святого Месропа Маштоца (2008, Армения).

awarded the Stalin Prize in 1952

1956, he was elected academician of the Armenian Academy of Sciences.

soon (at 24 years old!) He was elected a corresponding member of the USSR Academy of Sciences.

Награждён орденом Трудового Красного Знамени (1975). Лауреат Государственной премии СССР (1952).

corr. member of the National Academy of the Union of Soviet Socialist Republics (1953), acad.(1956).

rest
https://m.ru.armeniasputnik.am/columnists/20171217/9847855/nechistaya-matematika-ili-komu-ne-daval-pokoya-genij-mergelyana.html

Mergelian. Later, he entered the first Scientific Council on Cybernetics and his activities on YerRI MM organization found reflection in Yerevan society in the name of this institution as “Mergelian's institute”. In late 1957, a Computing Centre was organized as a part of the Armenian Academy of Sciences.

Science and Technology in Armenia

Electronics and Informatics Development in Armenian SSR (1960-1988)

http://rnas.asj-oa.am/view/people/==041C==0435==0440==0433==0435==043B==044F==043D=3A==0421=2E_==041D=2E=3A=3A.html

On a Conjecture of Mergelyan

The most general result on the approximation of functions by polynomials was obtained by S. N. Mergelyan [1], https://link.springer.com/article/10.3103/S1066369X13090028

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=8302&option_lang=eng

https://www.tandfonline.com/doi/full/10.1080/17476933.2013.837048

https://www.ams.org/journals/proc/1974-044-02/S0002-9939-1974-0361097-5/

https://www.jstor.org/stable/2309292